The area of an equilateral triangle is 9 sqrt | vedclass

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(B) The area of an equilateral triangle is given by the formula $\frac{\sqrt{3}}{4} 	imes 	ext{side}^{2}$.Given,$\frac{\sqrt{3}}{4} 	imes 	ext{sid

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$3 \sqrt{3}$

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(B) The area of an equilateral triangle is given by the formula $\frac{\sqrt{3}}{4} 	imes 	ext{side}^{2}$.Given,$\frac{\sqrt{3}}{4} 	imes 	ext{side}^{2} = 9 \sqrt{3}$.$\Rightarrow 	ext{side}^{2} = 9 	imes 4 = 36$.$\Rightarrow 	ext{side} = \sqrt{36} = 6 \ m$.In an equilateral triangle,the median is also the altitude. Let $AD$ be the median to side $BC$. Since $D$ is the midpoint of $BC$,$BD = \frac{6}{2} = 3 \ m$.Using the Pythagorean theorem in $	riangle ABD$:$AD = \sqrt{AB^{2} - BD^{2}} = \sqrt{6^{2} - 3^{2}}$.$AD = \sqrt{36 - 9} = \sqrt{27} = 3 \sqrt{3} \ m$.

The area of an equilateral triangle is $9 \sqrt{3} \ m^{2}$. The length (in $m$) of the median is

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